Shape Sequences

Welcome to the first lesson in your CEM 11+ Non-Verbal Reasoning course! Shape sequences are one of the most important NVR question types. In a sequence question you are shown a series of shapes that follow a pattern, and you must work out what comes next (or which shape fills a gap in the sequence).

In the CEM exam, NVR questions are interleaved with maths questions, so you may encounter a sequence question between two number problems. The shapes can be unfamiliar and the patterns may change from year to year, so learning a reliable strategy is essential.

What Is a Shape Sequence?

A shape sequence is a row of shapes (usually 4 or 5) arranged in order. Each shape changes from the one before it according to one or more rules. Your task is to identify those rules and predict the next shape.

Example

Position 1	Position 2	Position 3	Position 4	Position 5
Small white circle	Medium white circle	Large white circle	?

Here the rule is simple: the circle gets bigger at each step. The answer for position 4 would be an even larger white circle.

Properties That Can Change

When you look at a sequence, shapes can change in many different ways. Here are the main properties to watch:

Property	What to look for
Shape type	Does the shape change from a circle to a triangle to a square?
Size	Does the shape get bigger, smaller, or alternate?
Shading	Does the fill change (black, white, grey, striped, dotted)?
Rotation	Does the shape turn by a fixed amount (e.g. 45 or 90 degrees)?
Number of sides	Do the sides increase (triangle, square, pentagon, hexagon)?
Position	Does a dot, line, or small shape move around inside the main shape?
Number of elements	Does an extra line, dot, or shape get added each step?

Single-Rule Sequences

The simplest sequences change only one property at a time.

Worked Example 1 — Rotation

Step 1	Step 2	Step 3	Step 4	Step 5
Arrow pointing up	Arrow pointing right	Arrow pointing down	Arrow pointing left	?

Rule: The arrow rotates 90 degrees clockwise each step.

Answer: The arrow returns to pointing up (the pattern cycles every 4 steps).

Worked Example 2 — Shading Cycle

Step 1	Step 2	Step 3	Step 4	Step 5
Black square	Grey square	White square	Black square	?

Rule: The shading follows a three-step cycle: black, grey, white, then back to black.

Answer: Grey square.

Multi-Rule Sequences

In harder CEM questions, two or more properties change at the same time. You need to track each property separately.

Worked Example 3 — Size and Shading

Step 1	Step 2	Step 3	Step 4
Small black triangle	Large white triangle	Small black triangle	?

Rule 1 (size): Alternates between small and large.

Rule 2 (shading): Alternates between black and white.

Answer: Large white triangle (large because the previous was small; white because the previous was black).

Worked Example 4 — Sides Increase and Dot Moves

Step 1	Step 2	Step 3	Step 4
Triangle with a dot at the top	Square with a dot on the right	Pentagon with a dot at the bottom	?

Rule 1 (shape): The number of sides increases by 1 each step.

Rule 2 (dot position): The dot moves clockwise around the shape: top, right, bottom, left.

Answer: Hexagon (6 sides) with a dot on the left.

Cyclic vs Progressive Patterns

It is important to understand the difference between these two types of pattern:

Pattern type	How it works	Example
Progressive	A property keeps changing in one direction	Circle gets bigger and bigger at each step
Cyclic	A property repeats after a fixed number of steps	Shading goes black, grey, white, black, grey, white...

Many CEM sequences combine both. For instance, the number of sides might increase progressively (3, 4, 5, 6...) while the shading cycles (black, white, black, white...).

Step-by-Step Strategy

Follow these steps every time you see a sequence question:

Look across the whole row. Do not just look at two shapes — compare all of them.
List the properties. Write or think about each property: shape, size, colour, rotation, position, count.
Track each property. Note how each property changes from one step to the next.
Predict the next step. Apply each rule to generate the missing shape.
Check your answer. Make sure it fits every rule you have identified, then match it to the answer options.

CEM-Specific Tips

CEM papers often use unfamiliar or abstract shapes rather than simple circles and squares. Do not panic — the same rules of size, shading, rotation, and position still apply.
NVR questions are mixed in with maths, so you need to switch your thinking quickly. Stay focused and look for patterns straight away.
The format can vary from year to year. Sometimes you fill a gap in the middle of a sequence rather than finding the end.
Time pressure is a key challenge. Aim to spend about 30-40 seconds on each sequence question. If you are stuck, make a sensible guess and move on.

Key Terms

Term	Meaning
Sequence	A set of shapes arranged in order following a rule
Rule	The pattern or change that happens from one step to the next
Cycle	A pattern that repeats after a fixed number of steps
Progressive	A pattern that keeps changing in one direction (e.g. getting bigger)
Rotation	Turning a shape around a point
Shading	The fill of a shape (black, white, grey, striped, etc.)

Summary

Shape sequences ask you to find the pattern and predict what comes next. Check every property — shape, size, shading, rotation, position, and count. Track each property separately, especially when two or more rules are in play. Practise looking at unfamiliar shapes with confidence, and remember that the CEM exam can present sequences in unexpected ways. The more you practise, the faster you will spot the rules!